We compare the performances of different stepsizes by the required number of iterations to get convergence, by means of the performance profile [1]}. The cost of solving each problem is normalized based on the minimum cost for that problem, to get the performance ratio [1]}. The most efficient method solves the given problem with performance ratio 1, while all other methods solve it with a performance ratio at least 1. We plot the ratio of problems solved by a method within a certain factor of the smallest cost; this results in a cumulative distribution for each method. The algorithms are rated based on the maximum cost that one is willing to pay to get convergence. An infinite cost is assigned whenever a method is not able to solve a problem to the tolerance within the maximum number of iterations.
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